Giroud struck twice to see off the combative Championship outfit three days after his double in the 5-1 Premier League defeat of West Ham.

The France striker's performance drew praise from Wenger, but the Gunners manager conceded he still lacks sufficient cover up front, particularly with Gervinho away at the African Cup of Nations with Ivory Coast.

"It's good for Giroud's confidence. He's scored four goals this week and he had a few more chances here," Wenger said.

"He gets there. He has a presence in the box, he's dangerous and his physical presence was very important."

But asked whether he had sufficient strikers, he added: "Quality-wise no, number-wise, we could be a bit short maybe. Gervinho is not here at the moment.

"We have (Theo) Walcott, who can play through the middle and then of course Giroud."

With that in mind, Wenger is expected to attempt to bring in another striker before the end of the January transfer window, although he is not optimistic of completing a deal and denied he had moved for Fiorentina's Stevan Jovetic.

"You do not find them (strikers) in the street, the strikers that can play for us and strengthen our team. It's difficult in January," he said.

"In this kind of job it is realism that is important. Realistically I cannot tell you I will sign anyone tomorrow, or Tuesday, as we are not close to doing it."

Wenger opted to leave Walcott, Jack Wilshere and Santi Cazorla on the bench at Brighton but the plan almost back-fired.

Giroud twice put Arsenal ahead but Brighton recovered through Ashley Barnes and new signing Leonardo Ulloa and the Premier League side only secured victory thanks to a deflected late strike from Walcott.

"Of course I was worried. That is a gamble you take and you know it can backfire," Wenger said.

"I left a few out, for example Cazorla completely. But it was for medical reasons he couldn't play. It was very risky to play him. Jack, a little to protect his ankle.

"With the number of games we play, you cannot only play the same 11 in every single game.

"We play against Liverpool on Wednesday, Stoke on Saturday and then the players go away for international games.

"You have to rotate knowing that if it doesn't work you will be accused of having made the wrong decision."

Brighton boss Gus Poyet was please with the performance of Ulloa, who received international clearance following his move from Almeria just 24 hours before kick-off.

"To score in his first game for the club against Arsenal is always welcome. It is a good start for him," Poyet said.

"He will bring presence and strength, which is something we were missing, especially in matches when we have been the better team.

"I think Leo is going to have that kind of impact in the Championship for us without a doubt."

Despite Ulloa's encouraging debut, former Chelsea star Poyet admitted the overall mood in his dressing room was one of deep disappointment at a missed opportunity.

"It is funny feeling because we are more disappointed than we should be in the dressing room, it is like we had lost a final," he said.

"We had the chance to do something special, but when you lose players like we did to injury, against players like the quality of Arsenal, there is not much you can do.

"When you see Wilshere doing stretches and Walcott sprinting up and down on the sidelines ready to come on, you know you have got a problem."